3 citations · 3 across the 8 of their papers we have counts for
12 papers
On Traditional Menger and Rothberger Variations
Christopher Caruvana, Steven Clontz, Jared Holshouser
We present a comprehensive report on the relationships between variations of the Menger and Rothberger selection properties with respect to -covers and -covers in the most ge…
Non-Hausdorff Properties
Steven Clontz
Several weakenings of the property for topological spaces, including -Hausdorff, , weakly Hausdorff, semi-Hausdorff, , and , have been studied by mathematician…
Elementary submodels, coding strategies, and an infinite real number game
Will Brian, Steven Clontz
Matthew Baker investigated, in previous work, an elegant, infinite-length game that may be used to study subsets of real numbers. We present two accessible examples of how an impor…
On strategies for selection games related to countable dimension
Christopher Caruvana, Steven Clontz
Two selection games from the literature, and , are known to characterize countable dimension among certain spaces. Thi…
Metrizability of Mahavier products indexed by partial orders
Steven Clontz, Jacob Dunham
Let be separable metrizable, and let be a non-trivial relation on . For a given partial order , the Mahavier product (also…
Arhangelskii's -principles and selection games
Steven Clontz
Arhangelskii's properties and defined for convergent sequences may be characterized in terms of Scheeper's selection principles. We generalize these results to hold for…
On Ramsey properties, function spaces, and topological games
Steven Clontz, Alexander V. Osipov
An open question of Gruenhage asks if all strategically selectively separable spaces are Markov selectively separable, a game-theoretic statement known to hold for countable spaces…
Dual Selection Games
Steven Clontz
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strateg…
Limited Information Strategies and Discrete Selectivity
Steven Clontz, Jared Holshouser
We relate the property of discrete selectivity and its corresponding game, both recently introduced by V.V. Tkachuck, to a variety of selection principles and point picking games.…
Mahavier Products, Idempotent Relations, and Condition
Steven Clontz, Scott Varagona
Clearly, a generalized inverse limit of metrizable spaces indexed by is metrizable, as it is a subspace of a countable product of metrizable spaces. The authors previou…
Relating games of Menger, countable fan tightness, and selective separability
Steven Clontz
By adapting techniques of Arhangel'skii, Barman, and Dow, we may equate the existence of perfect-information, Markov, and tactical strategies between two interesting selection game…
Idempotent bonding relations are nontrivial if and only if they satisfy condition Gamma
Steven Clontz, Scott Varagona
A relation satisfies condition if there exist distinct with . The authors improve…